Problem: $f(x) = 3x^{2}-4$ What is the range of $f(x)$ ?
Solution: Consider the range of $3x^{2}$ The range of $x^2$ is $\{\, y \mid y \ge 0 \,\}$ Multiplying by $3$ doesn't change the range. To get $3x^{2}-4$, we subtract $4$. So the range becomes: $\{\, y \mid y ≥ -4 \,\}$.